Discrete Calculus

When Mathematica was first released in 1988, one of its significant achievements was the automation of traditional calculus. In a major feat of algorithmic development, Mathematica 7 now brings systematic automation to discrete calculus. Drawing on more than a century of disparate results in numerous fields, long-term R&D at Wolfram Research has led to innovations that for the first time allow coherent algorithmic treatment of discrete calculus. This achievement immediately makes possible new streamlined approaches to discrete problems in areas such as finance, actuarial science, statistics, combinatorics, algorithm analysis, information theory, numerical analysis, statistical physics, control theory and signal processing.